document.write( "Question 951103: Given that $\"+l%28x%29=+2sqrt+%28x%29-5+\"$ and $\"+m%28x%29=+sqrt+%28x%29-4+\"$ , determine the following combinations of functions in the simplest form and fill in the blank spaces by stating the combined function's domain and range.\r
\n" ); document.write( "\n" ); document.write( " $\"+%28l%29%2F%28m%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Very confused on what to do for this question. Would it just be:\r
\n" ); document.write( "\n" ); document.write( " $\"+%28l%28x%29%29%2F%28m%28x%29%29+=+%282sqrt+%28x%29-5%29%2F%28sqrt+%28x%29-4%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "How would you find the Domain and Range from that?\r
\n" ); document.write( "\n" ); document.write( "Thank you, \n" ); document.write( "

Algebra.Com's Answer #580777 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Domain is dictated by values that are not allowed.
\n" ); document.write( "So look at the denominator first.
\n" ); document.write( "The denominator cannot equal zero so,
\n" ); document.write( " $\"sqrt%28x%29-4=0\"$
\n" ); document.write( " $\"sqrt%28x%29=4\"$
\n" ); document.write( " $\"x=16\"$
\n" ); document.write( "So $\"x=16\"$ is excluded from the domain.
\n" ); document.write( "Also in the denominator, the argument for the square root must be non-negative so,
\n" ); document.write( " $\"x%3E=0\"$ .
\n" ); document.write( "Now look at the numerator, it has the same square root restriction as the denominator.
\n" ); document.write( "So then putting it all together.
\n" ); document.write( "Domain:[ $\"0\"$ , $\"16\"$ )U( $\"16\"$ , $\"infinity\"$ )
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\n" ); document.write( "For the range, look at the limit values from the domain,
\n" ); document.write( "When $\"x=0\"$ , $\"y=5%2F4\"$ .
\n" ); document.write( "As x increases towards 16, y decreases towards $\"-infinity\"$ .
\n" ); document.write( "When you approach 16 from the right, y increases towards $\"infinity\"$ .
\n" ); document.write( "When x approaches infinity, y approaches 2.
\n" ); document.write( "So then putting this all together,
\n" ); document.write( "Range : ( $\"-infinity\"$ , $\"5%2F4\"$ )U( $\"2\"$ , $\"infinity\"$ )
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\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C40%2C-25%2C25%2C%282sqrt%28x%29-5%29%2F%28sqrt%28x%29-4%29%29\"$
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